Navigation receivers that use global navigation satellite systems, such as GPS or GLONASS (hereinafter collectively referred to as “GNSS”), enable the highly accurate determination of the position of the receiver. The satellite signals comprise carrier harmonic signals that are modulated by pseudo-random binary codes and which, on the receive side, are used to measure the delay relative to a local reference clock. These delay measurements are used to determine the so-called pseudo-ranges between the receiver and the satellites. The pseudo-ranges are different from the true geometric ranges because the receiver's local clock is different from the satellite onboard clocks. If the number of satellites in sight is greater than or equal to four, then the measured pseudo-ranges can be processed to determine the user's single point location as represented by a vector X=(x, y, z)T, as well as to compensate for the receiver clock offset.
The need to improve positioning accuracies has eventually led to the development of differential navigation/positioning. In this mode, the user position is determined relative to the antenna connected to a base receiver, assuming that the coordinates of the base are known with high accuracy. The base receiver transmits its measurements (or corrections to the full measurements) to a mobile navigation receiver (or rover). The rover receiver uses these corrections to refine its own measurements in the course of data processing. The rationale for this approach is that since the pseudo-range measurement errors on the base and rover sides are strongly correlated, using differential measurements will substantially improve positioning accuracy.
Usually, the base is static and located at a known position. However, in relative navigation mode, both the base and rover are moving. In this mode, the user is interested in determining the vector between the base and the rover. In other words, the user is interested in determining the continuously changing rover position relative to the continuously changing position of the base. For example, when one aircraft or space vehicle is approaching another for in-flight refueling or docking, a highly accurate determination of relative position is important, while the absolute position of each vehicle is generally not critical.
The position of the rover changes continuously in time, and thus should be referenced to a time scale. The determination of the position of a mobile rover with respect to a base receiver in real-time is commonly referred to as the “Real-Time Kinematic” or RTK algorithm. As the name “real time kinematic” implies, the rover receiver is capable of calculating/outputting its precise position as soon as raw data measurements and differential corrections are available at the rover (i.e., practically instantly). The RTK mode uses a data communication link (typically either a radio communication link or a GSM binary data communication link), through which all the necessary information is transmitted from the base to the rover.
Further improvement of the accuracy in differential navigation/positioning applications can be achieved by using both the carrier phase and pseudorange measurements from the satellites to which the receivers are locked. If one measures the carrier phase of the signal received from a satellite in the base receiver and compares it with the carrier phase of the same satellite measured in the rover receiver, one can obtain measurement accuracy to within a small fraction of the carrier's wavelength, or to within centimeter level.
The practical implementation of this scheme runs into the problem of ambiguities in the phase measurements. The ambiguities are caused by the fact that the receiver computes the carrier phase via integration of the Doppler shift frequency, in which ambiguities appear as integration constants. The difference in the phase delays of a carrier signal received by the base and rover receivers is measured accurately within a constant number of wavelengths. Moreover, the difference of these constants between satellites is an integer number specific to each pair of satellites. These integer numbers are referred to as “integer ambiguities.” More precisely, one satellite is chosen as a “reference,” and pairs are formed between all satellites (except the reference) and the reference satellite. Determination of integer ambiguities is part of precise RTK algorithm execution. The RTK algorithm determines the set of all such integer numbers for all the satellites pairs being tracked, one integer part for each pair of satellites. The RTK algorithm determines this set along with other unknown values, which include rover coordinates and variations in the time scales. Determination of integer ambiguities is also known as “integer ambiguity resolution”.
Some existing GNSS satellite systems broadcast carriers in the L1 and L2 frequency bands. If the receiver processes the carrier signals in both of L1 and L2 bands, the number of satellite measurements channels increases correspondingly.
Two sets of raw measurements are measured by the base and rover receivers, respectively, and are used to determine the unknown state vector comprising three-dimensional position, clock shift, and the set of integer ambiguities. Each set of raw measurements includes the pseudo-range of each satellite to the receiver, and the full phase of each satellite carrier signal, the latter of which contains ambiguities. An observation vector is generated as the collection of the raw measurements for specific time instants known as “epochs”.
The relationship between the state vector and the observation vector is defined by a well-known system of navigation equations. See Appendix 1 for a detailed description. Given an observation vector, the system of equations may be solved to find the state vector if the number of equations equals or exceeds the number of unknowns in the state vector. In the latter case, conventional statistical methods may be used to solve the system: the least-squares method, and variations of recursive estimation, including well known methods of Kalman filtering, H∞ filtering, or l1 estimation, for example.
Practical real time implementations of methods for processing differential raw measurements may vary widely. The following sources of problems should be taken into account when assessing different approaches to real time processing:
Positioning Accuracy. This is the main objective in GNSS technology. Positioning accuracy is directly dependent on the accuracy of the raw measurements. The sources of errors affecting raw measurements can be divided into two groups. The first group roughly comprises spatially correlated errors. Differential navigation methods are aimed to compensate for those errors that simultaneously affect receivers located close to one another. The closer the distance between two antennas (the base and the rover), the better the compensation of common (correlated) errors. Well-known sources of such errors are ionospheric delays and ephemeris errors.
The second group of errors comprises spatially uncorrelated errors. Well known sources of this type of error are noise-like errors and multipath errors. Multipath errors are caused by reflection of the radio signal from surfaces located near the antenna. The antenna receives the direct signal running the shortest path from the satellite to the receiver, and also reflected signals following indirect paths. The combination of two (or more) signals at the antenna leads to the distortion of raw measurements. Multipath errors affect both pseudo-range and carrier phase measurements (see Appendix 1). The spatial correlation of multipath depends on the location of the reflection surface relative to the antenna. For surfaces generating reflections arriving at the upper side of the antenna, the carrier phase multipath happens to be substantially uncorrelated for antennas located only decimeters away. Owing to the uncorrelated nature of multipath errors, multiple antennas, connected to a multi-antenna receiver, can be used to improve the accuracy of raw measurements by averaging the measurements.
Availability of the position. Shading of signals coming from one or several satellites and tracked by the receiver may cause measurements to become unavailable. As a consequence, in conventional systems the receiver, working in either standalone or differential modes, can lose the ability to determine position. To remedy this defect one may try using multiple antennas, assuming that an obstacle shades not all antennas simultaneously. The position of the unknown shaded antenna may be derived from the known positions of other antennas of the receiver.
Speed of calculations. In developing positioning methods, one usually must find a compromise between the accuracy of the results and speed of calculations. It is desired to find an improved method to obtain accurate results for a given processing power.